Previous approaches to outdoor pose estimation differ in how they conduct the
search for estimates. Thompson and his group [14]
search position plus yaw angle by generating a sequence of
interpretations for the bearings. Since there are too many interpretations
(nm for m bearings and n peaks), they apply an alignment technique
to prune the search; they also concentrate the search on a few peaks of
high saliency. But high saliency peaks are generally large and far away;
estimates produced from detection of such peaks are bound to have large
errors, on the order of kilometers. Good accuracy requires the
use of large and small peaks in the horizon.

A different approach, which can handle large and small map features,
is adopted by Stein and Medioni [11]: they search in the
space of possible renderings of the map. The size of this space is also
large since each position leads to a different rendered
horizon. To reduce the size of this space, Stein and Medioni quantize the
rendered horizons and pre-compute large look-up hash tables containing
the quantized horizons. The performance of their approach depends on the
quantization; to attain realistic speeds, they report quantizations that
yield a minimum possible error of 300 meters.

Given the enormous number of correspondences between images and map,
a better approach is to search in the space of positions. Consider a Digital
Elevation Map gridded at 30 meters, covering a square of 6x6 kilometers.
To handle the full resolution of the map, we need to go through
40000 positions and establish a figure of merit for each one of them.
This seemingly daunting task has been pursued by Talluri and Aggarwal
[13]; to speed up the search, they have used a single point
in the image as a measure of ``goodness of fit'' between image and map.
Although easy to calculate, this is a unrealistic figure of merit since
images tend to have noise and, worse still, spurious features like rocks
or shadows.

We propose a new approach to this search problem that improves ideas reviewed
above. We search in the position space, but we construct a
figure of merit (the posterior probability described in
Section 4.2) that reflects the various
disturbances in the image
and can also include prior knowledge about position. The key idea is to
simplify the search procedure by pre-computing virtually all the calculations
that must be performed during search. We automatically create (off-line) a
table containing all the peaks that can be found in the map.
We also create (off-line) a table containing all the peaks that are visible
from every possible position. During search, we only have to access the
latter table for retrieving the index of visible peaks, access the former
table for retrieving characteristics of the peaks, and compute the
posterior probability for position. As an example, computation of the
posterior probability for the more than 30000 positions in the Pittsburgh
map of Figure 2 takes 3 seconds in a Sun Sparc20.